SOLUTION: Solve equation: log base 2 of X plus log base 2 of (3X+1) = 1 Answer in my book says, 2/3

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Question 980591: Solve equation:
log base 2 of X plus log base 2 of (3X+1) = 1

Answer in my book says, 2/3
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%28x%29%29%2Blog%282%2C%283x%2B1%29%29=1


log%282%2C%28x%2A%283x%2B1%29%29%29=1 Use rule 1


x%2A%283x%2B1%29=2%5E1


x%2A%283x%2B1%29=2


3x%5E2%2Bx=2


3x%5E2%2Bx-2=0


Use the quadratic formula to get the solutions x+=+2%2F3 or x+=+-1


The value x+=+-1 is NOT allowed because logs aren't defined when you plug in negative x values


The only solution is x+=+2%2F3


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+2%2Cx+%29+%2B+log%28+2%2C+3x+%2B+1+%29+=+1+
Convert +1+ to a log to base 2
+log%28+2%2Cx+%29+%2B+log%28+2%2C+3x+%2B+1+%29+=+log%28+2%2C2+%29+
+log%28+2%2C+x%2A%28+3x+%2B+1+%29+%29+=+log%28+2%2C2+%29+
+x%2A%28+3x+%2B+1+%29+=+2+
+3x%5E2+%2B+x+=+2+
+3x%5E2+%2B+x+-+2+=+0+
Use quadratic equation:
+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+x+=+%28+-1+%2B-+sqrt%28+1%5E2-4%2A3%2A%28-2%29+%29%29%2F%282%2A3%29+
+x+=+%28+-1+%2B-+sqrt%28+1+%2B+24+%29%29+%2F+6+
+x+=+%28+-1+%2B-+sqrt%28+25+%29%29+%2F+6+
+x+=+%28+-1+%2B+5+%29+%2F+6+
+x+=+4%2F6+
+x+=+2%2F3+
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Using the negative square root:
+x+=+%28+-1+-+5+%29+%2F+6+
+x+=+-6%2F6+
+x+=+-1+